Simulation of fractionated electrograms at low spatial resolution in large-scale heart models

To compute extracellular potentials from transmembrane potentials an elliptic boundary-value problem must be solved. This must be done at a spatial resolution of 0.2 mm or better to avoid artefacts in the form of large spikes before and after major deflections. For macroscopic heart models, this leads to very large linear systems. Artefacts in low-resolution solutions are related to the restriction operator that is used to translate the sources from high to low resolution. Typically, this restriction is done by injecting transmembrane potentials. We propose to use transmembrane current as a source, with weighted summation rather than simple injection. We tested this method in a model of the human ventricles. We found that using the proposed scheme, a good visual match could be obtained between electrograms computed at 1-mm and 0.2-mm resolution, even in regions where strong sub-millimeter heterogeneity in tissue conductivity was present.